Data.Random.Distribution

Documentation

class Distribution d t where

A Distribution is a data representation of a random variable's probability structure. For example, in Data.Random.Distribution.Normal, the Normal distribution is defined as:

data Normal a
    = StdNormal
    | Normal a a

Where the two parameters of the Normal data constructor are the mean and standard deviation of the random variable, respectively. To make use of the Normal type, one can convert it to an rvar and manipulate it or sample it directly:

x <- sample (rvar (Normal 10 2))
x <- sample (Normal 10 2)

A Distribution is typically more transparent than an RVar but less composable (precisely because of that transparency). There are several practical uses for types implementing Distribution:

• Typically, a Distribution will expose several parameters of a standard mathematical model of a probability distribution, such as mean and std deviation for the normal distribution. Thus, they can be manipulated analytically using mathematical insights about the distributions they represent. For example, a collection of bernoulli variables could be simplified into a (hopefully) smaller collection of binomial variables.
• Because they are generally just containers for parameters, they can be easily serialized to persistent storage or read from user-supplied configurations (eg, initialization data for a simulation).
• If a type additionally implements the CDF subclass, which extends Distribution with a cumulative density function, an arbitrary random variable x can be tested against the distribution by testing fmap (cdf dist) x for uniformity.

On the other hand, most Distributions will not be closed under all the same operations as RVar (which, being a monad, has a fully turing-complete internal computational model). The sum of two uniformly-distributed variables, for example, is not uniformly distributed. To support general composition, the Distribution class defines a function rvar to construct the more-abstract and more-composable RVar representation of a random variable.

Methods

rvar :: d t -> RVar t

Return a random variable with this distribution.

rvarT :: d t -> RVarT n t

Return a random variable with the given distribution, pre-lifted to an arbitrary RVarT. Any arbitrary RVar can also be converted to an 'RVarT m' for an arbitrary m, using either lift or sample.

Instances

Distribution StdUniform Bool

Methods

rvar :: StdUniform Bool -> RVar Bool

rvarT :: StdUniform Bool -> RVarT n Bool

Distribution StdUniform Char

Methods

rvar :: StdUniform Char -> RVar Char

rvarT :: StdUniform Char -> RVarT n Char

Distribution StdUniform Double

Methods

rvar :: StdUniform Double -> RVar Double

rvarT :: StdUniform Double -> RVarT n Double

Distribution StdUniform Float

Methods

rvar :: StdUniform Float -> RVar Float

rvarT :: StdUniform Float -> RVarT n Float

Distribution StdUniform Int

Methods

rvar :: StdUniform Int -> RVar Int

rvarT :: StdUniform Int -> RVarT n Int

Distribution StdUniform Int8

Methods

rvar :: StdUniform Int8 -> RVar Int8

rvarT :: StdUniform Int8 -> RVarT n Int8

Distribution StdUniform Int16

Methods

rvar :: StdUniform Int16 -> RVar Int16

rvarT :: StdUniform Int16 -> RVarT n Int16

Distribution StdUniform Int32

Methods

rvar :: StdUniform Int32 -> RVar Int32

rvarT :: StdUniform Int32 -> RVarT n Int32

Distribution StdUniform Int64

Methods

rvar :: StdUniform Int64 -> RVar Int64

rvarT :: StdUniform Int64 -> RVarT n Int64

Distribution StdUniform Ordering

Methods

rvar :: StdUniform Ordering -> RVar Ordering

rvarT :: StdUniform Ordering -> RVarT n Ordering

Distribution StdUniform Word

Methods

rvar :: StdUniform Word -> RVar Word

rvarT :: StdUniform Word -> RVarT n Word

Distribution StdUniform Word8

Methods

rvar :: StdUniform Word8 -> RVar Word8

rvarT :: StdUniform Word8 -> RVarT n Word8

Distribution StdUniform Word16

Methods

rvar :: StdUniform Word16 -> RVar Word16

rvarT :: StdUniform Word16 -> RVarT n Word16

Distribution StdUniform Word32

Methods

rvar :: StdUniform Word32 -> RVar Word32

rvarT :: StdUniform Word32 -> RVarT n Word32

Distribution StdUniform Word64

Methods

rvar :: StdUniform Word64 -> RVar Word64

rvarT :: StdUniform Word64 -> RVarT n Word64

Distribution StdUniform ()

Methods

rvar :: StdUniform () -> RVar ()

rvarT :: StdUniform () -> RVarT n ()

Distribution Uniform Bool

Methods

rvar :: Uniform Bool -> RVar Bool

rvarT :: Uniform Bool -> RVarT n Bool

Distribution Uniform Char

Methods

rvar :: Uniform Char -> RVar Char

rvarT :: Uniform Char -> RVarT n Char

Distribution Uniform Double

Methods

rvar :: Uniform Double -> RVar Double

rvarT :: Uniform Double -> RVarT n Double

Distribution Uniform Float

Methods

rvar :: Uniform Float -> RVar Float

rvarT :: Uniform Float -> RVarT n Float

Distribution Uniform Int

Methods

rvar :: Uniform Int -> RVar Int

rvarT :: Uniform Int -> RVarT n Int

Distribution Uniform Int8

Methods

rvar :: Uniform Int8 -> RVar Int8

rvarT :: Uniform Int8 -> RVarT n Int8

Distribution Uniform Int16

Methods

rvar :: Uniform Int16 -> RVar Int16

rvarT :: Uniform Int16 -> RVarT n Int16

Distribution Uniform Int32

Methods

rvar :: Uniform Int32 -> RVar Int32

rvarT :: Uniform Int32 -> RVarT n Int32

Distribution Uniform Int64

Methods

rvar :: Uniform Int64 -> RVar Int64

rvarT :: Uniform Int64 -> RVarT n Int64

Distribution Uniform Integer

Methods

rvar :: Uniform Integer -> RVar Integer

rvarT :: Uniform Integer -> RVarT n Integer

Distribution Uniform Ordering

Methods

rvar :: Uniform Ordering -> RVar Ordering

rvarT :: Uniform Ordering -> RVarT n Ordering

Distribution Uniform Word

Methods

rvar :: Uniform Word -> RVar Word

rvarT :: Uniform Word -> RVarT n Word

Distribution Uniform Word8

Methods

rvar :: Uniform Word8 -> RVar Word8

rvarT :: Uniform Word8 -> RVarT n Word8

Distribution Uniform Word16

Methods

rvar :: Uniform Word16 -> RVar Word16

rvarT :: Uniform Word16 -> RVarT n Word16

Distribution Uniform Word32

Methods

rvar :: Uniform Word32 -> RVar Word32

rvarT :: Uniform Word32 -> RVarT n Word32

Distribution Uniform Word64

Methods

rvar :: Uniform Word64 -> RVar Word64

rvarT :: Uniform Word64 -> RVarT n Word64

Distribution Uniform ()

Methods

rvar :: Uniform () -> RVar ()

rvarT :: Uniform () -> RVarT n ()

(Floating a, Distribution StdUniform a) => Distribution Exponential a

Methods

rvar :: Exponential a -> RVar a

rvarT :: Exponential a -> RVarT n a

(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a

Methods

rvar :: StretchedExponential a -> RVar a

rvarT :: StretchedExponential a -> RVarT n a

Distribution Normal Double

Methods

rvar :: Normal Double -> RVar Double

rvarT :: Normal Double -> RVarT n Double

Distribution Normal Float

Methods

rvar :: Normal Float -> RVar Float

rvarT :: Normal Float -> RVarT n Float

(Floating a, Ord a, Distribution Normal a, Distribution StdUniform a) => Distribution Gamma a

Methods

rvar :: Gamma a -> RVar a

rvarT :: Gamma a -> RVarT n a

Distribution Beta Double

Methods

rvar :: Beta Double -> RVar Double

rvarT :: Beta Double -> RVarT n Double

Distribution Beta Float

Methods

rvar :: Beta Float -> RVar Float

rvarT :: Beta Float -> RVarT n Float

(Fractional t, Distribution Gamma t) => Distribution ChiSquare t

Methods

rvar :: ChiSquare t -> RVar t

rvarT :: ChiSquare t -> RVarT n t

(RealFloat a, Distribution StdUniform a) => Distribution Rayleigh a

Methods

rvar :: Rayleigh a -> RVar a

rvarT :: Rayleigh a -> RVarT n a

(Floating a, Distribution Normal a, Distribution ChiSquare a) => Distribution T a

Methods

rvar :: T a -> RVar a

rvarT :: T a -> RVarT n a

(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a

Methods

rvar :: Triangular a -> RVar a

rvarT :: Triangular a -> RVarT n a

(Floating a, Distribution StdUniform a) => Distribution Weibull a

Methods

rvar :: Weibull a -> RVar a

rvarT :: Weibull a -> RVarT n a

(Floating a, Distribution StdUniform a) => Distribution Pareto a

Methods

rvar :: Pareto a -> RVar a

rvarT :: Pareto a -> RVarT n a

HasResolution r => Distribution StdUniform (Fixed r)

Methods

rvar :: StdUniform (Fixed r) -> RVar (Fixed r)

rvarT :: StdUniform (Fixed r) -> RVarT n (Fixed r)

HasResolution r => Distribution Uniform (Fixed r)

Methods

rvar :: Uniform (Fixed r) -> RVar (Fixed r)

rvarT :: Uniform (Fixed r) -> RVarT n (Fixed r)

(Fractional a, Distribution Gamma a) => Distribution Dirichlet [a]

Methods

rvar :: Dirichlet [a] -> RVar [a]

rvarT :: Dirichlet [a] -> RVarT n [a]

(Ord a, Fractional a, Distribution StdUniform a) => Distribution StdSimplex [a]

Methods

rvar :: StdSimplex [a] -> RVar [a]

rvarT :: StdSimplex [a] -> RVarT n [a]

(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool

Methods

rvar :: Bernoulli b Bool -> RVar Bool

rvarT :: Bernoulli b Bool -> RVarT n Bool

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word64

Methods

rvar :: Bernoulli b0 Word64 -> RVar Word64

rvarT :: Bernoulli b0 Word64 -> RVarT n Word64

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word32

Methods

rvar :: Bernoulli b0 Word32 -> RVar Word32

rvarT :: Bernoulli b0 Word32 -> RVarT n Word32

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word16

Methods

rvar :: Bernoulli b0 Word16 -> RVar Word16

rvarT :: Bernoulli b0 Word16 -> RVarT n Word16

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word8

Methods

rvar :: Bernoulli b0 Word8 -> RVar Word8

rvarT :: Bernoulli b0 Word8 -> RVarT n Word8

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word

Methods

rvar :: Bernoulli b0 Word -> RVar Word

rvarT :: Bernoulli b0 Word -> RVarT n Word

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int64

Methods

rvar :: Bernoulli b0 Int64 -> RVar Int64

rvarT :: Bernoulli b0 Int64 -> RVarT n Int64

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int32

Methods

rvar :: Bernoulli b0 Int32 -> RVar Int32

rvarT :: Bernoulli b0 Int32 -> RVarT n Int32

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int16

Methods

rvar :: Bernoulli b0 Int16 -> RVar Int16

rvarT :: Bernoulli b0 Int16 -> RVarT n Int16

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int8

Methods

rvar :: Bernoulli b0 Int8 -> RVar Int8

rvarT :: Bernoulli b0 Int8 -> RVarT n Int8

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int

Methods

rvar :: Bernoulli b0 Int -> RVar Int

rvarT :: Bernoulli b0 Int -> RVarT n Int

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Integer

Methods

rvar :: Bernoulli b0 Integer -> RVar Integer

rvarT :: Bernoulli b0 Integer -> RVarT n Integer

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Double

Methods

rvar :: Bernoulli b0 Double -> RVar Double

rvarT :: Bernoulli b0 Double -> RVarT n Double

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Float

Methods

rvar :: Bernoulli b0 Float -> RVar Float

rvarT :: Bernoulli b0 Float -> RVarT n Float

(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a

Methods

rvar :: Categorical p a -> RVar a

rvarT :: Categorical p a -> RVarT n a

(Num t, Ord t, Vector v t) => Distribution (Ziggurat v) t

Methods

rvar :: Ziggurat v t -> RVar t

rvarT :: Ziggurat v t -> RVarT n t

(Integral a, Floating b, Ord b, Distribution Normal b, Distribution StdUniform b) => Distribution (Erlang a) b

Methods

rvar :: Erlang a b -> RVar b

rvarT :: Erlang a b -> RVarT n b

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word64

Methods

rvar :: Binomial b0 Word64 -> RVar Word64

rvarT :: Binomial b0 Word64 -> RVarT n Word64

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word32

Methods

rvar :: Binomial b0 Word32 -> RVar Word32

rvarT :: Binomial b0 Word32 -> RVarT n Word32

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word16

Methods

rvar :: Binomial b0 Word16 -> RVar Word16

rvarT :: Binomial b0 Word16 -> RVarT n Word16

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word8

Methods

rvar :: Binomial b0 Word8 -> RVar Word8

rvarT :: Binomial b0 Word8 -> RVarT n Word8

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word

Methods

rvar :: Binomial b0 Word -> RVar Word

rvarT :: Binomial b0 Word -> RVarT n Word

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int64

Methods

rvar :: Binomial b0 Int64 -> RVar Int64

rvarT :: Binomial b0 Int64 -> RVarT n Int64

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int32

Methods

rvar :: Binomial b0 Int32 -> RVar Int32

rvarT :: Binomial b0 Int32 -> RVarT n Int32

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int16

Methods

rvar :: Binomial b0 Int16 -> RVar Int16

rvarT :: Binomial b0 Int16 -> RVarT n Int16

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int8

Methods

rvar :: Binomial b0 Int8 -> RVar Int8

rvarT :: Binomial b0 Int8 -> RVarT n Int8

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int

Methods

rvar :: Binomial b0 Int -> RVar Int

rvarT :: Binomial b0 Int -> RVarT n Int

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Integer

Methods

rvar :: Binomial b0 Integer -> RVar Integer

rvarT :: Binomial b0 Integer -> RVarT n Integer

Distribution (Binomial b0) Integer => Distribution (Binomial b0) Double

Methods

rvar :: Binomial b0 Double -> RVar Double

rvarT :: Binomial b0 Double -> RVarT n Double

Distribution (Binomial b0) Integer => Distribution (Binomial b0) Float

Methods

rvar :: Binomial b0 Float -> RVar Float

rvarT :: Binomial b0 Float -> RVarT n Float

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word64) b0, Distribution (Binomial b0) Word64) => Distribution (Poisson b0) Word64

Methods

rvar :: Poisson b0 Word64 -> RVar Word64

rvarT :: Poisson b0 Word64 -> RVarT n Word64

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word32) b0, Distribution (Binomial b0) Word32) => Distribution (Poisson b0) Word32

Methods

rvar :: Poisson b0 Word32 -> RVar Word32

rvarT :: Poisson b0 Word32 -> RVarT n Word32

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word16) b0, Distribution (Binomial b0) Word16) => Distribution (Poisson b0) Word16

Methods

rvar :: Poisson b0 Word16 -> RVar Word16

rvarT :: Poisson b0 Word16 -> RVarT n Word16

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word8) b0, Distribution (Binomial b0) Word8) => Distribution (Poisson b0) Word8

Methods

rvar :: Poisson b0 Word8 -> RVar Word8

rvarT :: Poisson b0 Word8 -> RVarT n Word8

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word) b0, Distribution (Binomial b0) Word) => Distribution (Poisson b0) Word

Methods

rvar :: Poisson b0 Word -> RVar Word

rvarT :: Poisson b0 Word -> RVarT n Word

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int64) b0, Distribution (Binomial b0) Int64) => Distribution (Poisson b0) Int64

Methods

rvar :: Poisson b0 Int64 -> RVar Int64

rvarT :: Poisson b0 Int64 -> RVarT n Int64

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int32) b0, Distribution (Binomial b0) Int32) => Distribution (Poisson b0) Int32

Methods

rvar :: Poisson b0 Int32 -> RVar Int32

rvarT :: Poisson b0 Int32 -> RVarT n Int32

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int16) b0, Distribution (Binomial b0) Int16) => Distribution (Poisson b0) Int16

Methods

rvar :: Poisson b0 Int16 -> RVar Int16

rvarT :: Poisson b0 Int16 -> RVarT n Int16

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int8) b0, Distribution (Binomial b0) Int8) => Distribution (Poisson b0) Int8

Methods

rvar :: Poisson b0 Int8 -> RVar Int8

rvarT :: Poisson b0 Int8 -> RVarT n Int8

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int) b0, Distribution (Binomial b0) Int) => Distribution (Poisson b0) Int

Methods

rvar :: Poisson b0 Int -> RVar Int

rvarT :: Poisson b0 Int -> RVarT n Int

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Integer) b0, Distribution (Binomial b0) Integer) => Distribution (Poisson b0) Integer

Methods

rvar :: Poisson b0 Integer -> RVar Integer

rvarT :: Poisson b0 Integer -> RVarT n Integer

Distribution (Poisson b0) Integer => Distribution (Poisson b0) Double

Methods

rvar :: Poisson b0 Double -> RVar Double

rvarT :: Poisson b0 Double -> RVarT n Double

Distribution (Poisson b0) Integer => Distribution (Poisson b0) Float

Methods

rvar :: Poisson b0 Float -> RVar Float

rvarT :: Poisson b0 Float -> RVarT n Float

(Distribution (Bernoulli b) Bool, RealFloat a) => Distribution (Bernoulli b) (Complex a)

Methods

rvar :: Bernoulli b (Complex a) -> RVar (Complex a)

rvarT :: Bernoulli b (Complex a) -> RVarT n (Complex a)

(Distribution (Bernoulli b) Bool, Integral a) => Distribution (Bernoulli b) (Ratio a)

Methods

rvar :: Bernoulli b (Ratio a) -> RVar (Ratio a)

rvarT :: Bernoulli b (Ratio a) -> RVarT n (Ratio a)

(Num a, Eq a, Fractional p, Distribution (Binomial p) a) => Distribution (Multinomial p) [a]

Methods

rvar :: Multinomial p [a] -> RVar [a]

rvarT :: Multinomial p [a] -> RVarT n [a]

class Distribution d t => PDF d t where

Methods

pdf :: d t -> t -> Double

logPdf :: d t -> t -> Double

Instances

PDF StdUniform Double

Methods

pdf :: StdUniform Double -> Double -> Double

logPdf :: StdUniform Double -> Double -> Double

PDF StdUniform Float

Methods

pdf :: StdUniform Float -> Float -> Double

logPdf :: StdUniform Float -> Float -> Double

(Real a, Floating a, Distribution Normal a) => PDF Normal a

Methods

pdf :: Normal a -> a -> Double

logPdf :: Normal a -> a -> Double

PDF Beta Double

Methods

pdf :: Beta Double -> Double -> Double

logPdf :: Beta Double -> Double -> Double

PDF Beta Float

Methods

pdf :: Beta Float -> Float -> Double

logPdf :: Beta Float -> Float -> Double

(Real b0, Distribution (Binomial b0) Word64) => PDF (Binomial b0) Word64

Methods

pdf :: Binomial b0 Word64 -> Word64 -> Double

logPdf :: Binomial b0 Word64 -> Word64 -> Double

(Real b0, Distribution (Binomial b0) Word32) => PDF (Binomial b0) Word32

Methods

pdf :: Binomial b0 Word32 -> Word32 -> Double

logPdf :: Binomial b0 Word32 -> Word32 -> Double

(Real b0, Distribution (Binomial b0) Word16) => PDF (Binomial b0) Word16

Methods

pdf :: Binomial b0 Word16 -> Word16 -> Double

logPdf :: Binomial b0 Word16 -> Word16 -> Double

(Real b0, Distribution (Binomial b0) Word8) => PDF (Binomial b0) Word8

Methods

pdf :: Binomial b0 Word8 -> Word8 -> Double

logPdf :: Binomial b0 Word8 -> Word8 -> Double

(Real b0, Distribution (Binomial b0) Word) => PDF (Binomial b0) Word

Methods

pdf :: Binomial b0 Word -> Word -> Double

logPdf :: Binomial b0 Word -> Word -> Double

(Real b0, Distribution (Binomial b0) Int64) => PDF (Binomial b0) Int64

Methods

pdf :: Binomial b0 Int64 -> Int64 -> Double

logPdf :: Binomial b0 Int64 -> Int64 -> Double

(Real b0, Distribution (Binomial b0) Int32) => PDF (Binomial b0) Int32

Methods

pdf :: Binomial b0 Int32 -> Int32 -> Double

logPdf :: Binomial b0 Int32 -> Int32 -> Double

(Real b0, Distribution (Binomial b0) Int16) => PDF (Binomial b0) Int16

Methods

pdf :: Binomial b0 Int16 -> Int16 -> Double

logPdf :: Binomial b0 Int16 -> Int16 -> Double

(Real b0, Distribution (Binomial b0) Int8) => PDF (Binomial b0) Int8

Methods

pdf :: Binomial b0 Int8 -> Int8 -> Double

logPdf :: Binomial b0 Int8 -> Int8 -> Double

(Real b0, Distribution (Binomial b0) Int) => PDF (Binomial b0) Int

Methods

pdf :: Binomial b0 Int -> Int -> Double

logPdf :: Binomial b0 Int -> Int -> Double

(Real b0, Distribution (Binomial b0) Integer) => PDF (Binomial b0) Integer

Methods

pdf :: Binomial b0 Integer -> Integer -> Double

logPdf :: Binomial b0 Integer -> Integer -> Double

PDF (Binomial b0) Integer => PDF (Binomial b0) Double

Methods

pdf :: Binomial b0 Double -> Double -> Double

logPdf :: Binomial b0 Double -> Double -> Double

PDF (Binomial b0) Integer => PDF (Binomial b0) Float

Methods

pdf :: Binomial b0 Float -> Float -> Double

logPdf :: Binomial b0 Float -> Float -> Double

class Distribution d t => CDF d t where

Minimal complete definition

cdf

Methods

cdf :: d t -> t -> Double

Return the cumulative distribution function of this distribution. That is, a function taking x :: t to the probability that the next sample will return a value less than or equal to x, according to some order or partial order (not necessarily an obvious one).

In the case where t is an instance of Ord, cdf should correspond to the CDF with respect to that order.

In other cases, cdf is only required to satisfy the following law: fmap (cdf d) (rvar d) must be uniformly distributed over (0,1). Inclusion of either endpoint is optional, though the preferred range is (0,1].

Note that this definition requires that cdf for a product type should _not_ be a joint CDF as commonly defined, as that definition violates both conditions. Instead, it should be a univariate CDF over the product type. That is, it should represent the CDF with respect to the lexicographic order of the product.

The present specification is probably only really useful for testing conformance of a variable to its target distribution, and I am open to suggestions for more-useful specifications (especially with regard to the interaction with product types).

Instances

CDF StdUniform Bool

Methods

cdf :: StdUniform Bool -> Bool -> Double

CDF StdUniform Char

Methods

cdf :: StdUniform Char -> Char -> Double

CDF StdUniform Double

Methods

cdf :: StdUniform Double -> Double -> Double

CDF StdUniform Float

Methods

cdf :: StdUniform Float -> Float -> Double

CDF StdUniform Int

Methods

cdf :: StdUniform Int -> Int -> Double

CDF StdUniform Int8

Methods

cdf :: StdUniform Int8 -> Int8 -> Double

CDF StdUniform Int16

Methods

cdf :: StdUniform Int16 -> Int16 -> Double

CDF StdUniform Int32

Methods

cdf :: StdUniform Int32 -> Int32 -> Double

CDF StdUniform Int64

Methods

cdf :: StdUniform Int64 -> Int64 -> Double

CDF StdUniform Ordering

Methods

cdf :: StdUniform Ordering -> Ordering -> Double

CDF StdUniform Word

Methods

cdf :: StdUniform Word -> Word -> Double

CDF StdUniform Word8

Methods

cdf :: StdUniform Word8 -> Word8 -> Double

CDF StdUniform Word16

Methods

cdf :: StdUniform Word16 -> Word16 -> Double

CDF StdUniform Word32

Methods

cdf :: StdUniform Word32 -> Word32 -> Double

CDF StdUniform Word64

Methods

cdf :: StdUniform Word64 -> Word64 -> Double

CDF StdUniform ()

Methods

cdf :: StdUniform () -> () -> Double

CDF Uniform Bool

Methods

cdf :: Uniform Bool -> Bool -> Double

CDF Uniform Char

Methods

cdf :: Uniform Char -> Char -> Double

CDF Uniform Double

Methods

cdf :: Uniform Double -> Double -> Double

CDF Uniform Float

Methods

cdf :: Uniform Float -> Float -> Double

CDF Uniform Int

Methods

cdf :: Uniform Int -> Int -> Double

CDF Uniform Int8

Methods

cdf :: Uniform Int8 -> Int8 -> Double

CDF Uniform Int16

Methods

cdf :: Uniform Int16 -> Int16 -> Double

CDF Uniform Int32

Methods

cdf :: Uniform Int32 -> Int32 -> Double

CDF Uniform Int64

Methods

cdf :: Uniform Int64 -> Int64 -> Double

CDF Uniform Integer

Methods

cdf :: Uniform Integer -> Integer -> Double

CDF Uniform Ordering

Methods

cdf :: Uniform Ordering -> Ordering -> Double

CDF Uniform Word

Methods

cdf :: Uniform Word -> Word -> Double

CDF Uniform Word8

Methods

cdf :: Uniform Word8 -> Word8 -> Double

CDF Uniform Word16

Methods

cdf :: Uniform Word16 -> Word16 -> Double

CDF Uniform Word32

Methods

cdf :: Uniform Word32 -> Word32 -> Double

CDF Uniform Word64

Methods

cdf :: Uniform Word64 -> Word64 -> Double

CDF Uniform ()

Methods

cdf :: Uniform () -> () -> Double

(Real a, Distribution Exponential a) => CDF Exponential a

Methods

cdf :: Exponential a -> a -> Double

(Real a, Distribution StretchedExponential a) => CDF StretchedExponential a

Methods

cdf :: StretchedExponential a -> a -> Double

(Real a, Distribution Normal a) => CDF Normal a

Methods

cdf :: Normal a -> a -> Double

(Real a, Distribution Gamma a) => CDF Gamma a

Methods

cdf :: Gamma a -> a -> Double

(Real t, Distribution ChiSquare t) => CDF ChiSquare t

Methods

cdf :: ChiSquare t -> t -> Double

(Real a, Distribution Rayleigh a) => CDF Rayleigh a

Methods

cdf :: Rayleigh a -> a -> Double

(Real a, Distribution T a) => CDF T a

Methods

cdf :: T a -> a -> Double

(RealFrac a, Distribution Triangular a) => CDF Triangular a

Methods

cdf :: Triangular a -> a -> Double

(Real a, Distribution Weibull a) => CDF Weibull a

Methods

cdf :: Weibull a -> a -> Double

(Real a, Distribution Pareto a) => CDF Pareto a

Methods

cdf :: Pareto a -> a -> Double

HasResolution r => CDF StdUniform (Fixed r)

Methods

cdf :: StdUniform (Fixed r) -> Fixed r -> Double

HasResolution r => CDF Uniform (Fixed r)

Methods

cdf :: Uniform (Fixed r) -> Fixed r -> Double

(Distribution (Bernoulli b) Bool, Real b) => CDF (Bernoulli b) Bool

Methods

cdf :: Bernoulli b Bool -> Bool -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word64

Methods

cdf :: Bernoulli b0 Word64 -> Word64 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word32

Methods

cdf :: Bernoulli b0 Word32 -> Word32 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word16

Methods

cdf :: Bernoulli b0 Word16 -> Word16 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word8

Methods

cdf :: Bernoulli b0 Word8 -> Word8 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word

Methods

cdf :: Bernoulli b0 Word -> Word -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int64

Methods

cdf :: Bernoulli b0 Int64 -> Int64 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int32

Methods

cdf :: Bernoulli b0 Int32 -> Int32 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int16

Methods

cdf :: Bernoulli b0 Int16 -> Int16 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int8

Methods

cdf :: Bernoulli b0 Int8 -> Int8 -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int

Methods

cdf :: Bernoulli b0 Int -> Int -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Integer

Methods

cdf :: Bernoulli b0 Integer -> Integer -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Double

Methods

cdf :: Bernoulli b0 Double -> Double -> Double

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Float

Methods

cdf :: Bernoulli b0 Float -> Float -> Double

(Integral a, Real b, Distribution (Erlang a) b) => CDF (Erlang a) b

Methods

cdf :: Erlang a b -> b -> Double

(Real b0, Distribution (Binomial b0) Word64) => CDF (Binomial b0) Word64

Methods

cdf :: Binomial b0 Word64 -> Word64 -> Double

(Real b0, Distribution (Binomial b0) Word32) => CDF (Binomial b0) Word32

Methods

cdf :: Binomial b0 Word32 -> Word32 -> Double

(Real b0, Distribution (Binomial b0) Word16) => CDF (Binomial b0) Word16

Methods

cdf :: Binomial b0 Word16 -> Word16 -> Double

(Real b0, Distribution (Binomial b0) Word8) => CDF (Binomial b0) Word8

Methods

cdf :: Binomial b0 Word8 -> Word8 -> Double

(Real b0, Distribution (Binomial b0) Word) => CDF (Binomial b0) Word

Methods

cdf :: Binomial b0 Word -> Word -> Double

(Real b0, Distribution (Binomial b0) Int64) => CDF (Binomial b0) Int64

Methods

cdf :: Binomial b0 Int64 -> Int64 -> Double

(Real b0, Distribution (Binomial b0) Int32) => CDF (Binomial b0) Int32

Methods

cdf :: Binomial b0 Int32 -> Int32 -> Double

(Real b0, Distribution (Binomial b0) Int16) => CDF (Binomial b0) Int16

Methods

cdf :: Binomial b0 Int16 -> Int16 -> Double

(Real b0, Distribution (Binomial b0) Int8) => CDF (Binomial b0) Int8

Methods

cdf :: Binomial b0 Int8 -> Int8 -> Double

(Real b0, Distribution (Binomial b0) Int) => CDF (Binomial b0) Int

Methods

cdf :: Binomial b0 Int -> Int -> Double

(Real b0, Distribution (Binomial b0) Integer) => CDF (Binomial b0) Integer

Methods

cdf :: Binomial b0 Integer -> Integer -> Double

CDF (Binomial b0) Integer => CDF (Binomial b0) Double

Methods

cdf :: Binomial b0 Double -> Double -> Double

CDF (Binomial b0) Integer => CDF (Binomial b0) Float

Methods

cdf :: Binomial b0 Float -> Float -> Double

(Real b0, Distribution (Poisson b0) Word64) => CDF (Poisson b0) Word64

Methods

cdf :: Poisson b0 Word64 -> Word64 -> Double

(Real b0, Distribution (Poisson b0) Word32) => CDF (Poisson b0) Word32

Methods

cdf :: Poisson b0 Word32 -> Word32 -> Double

(Real b0, Distribution (Poisson b0) Word16) => CDF (Poisson b0) Word16

Methods

cdf :: Poisson b0 Word16 -> Word16 -> Double

(Real b0, Distribution (Poisson b0) Word8) => CDF (Poisson b0) Word8

Methods

cdf :: Poisson b0 Word8 -> Word8 -> Double

(Real b0, Distribution (Poisson b0) Word) => CDF (Poisson b0) Word

Methods

cdf :: Poisson b0 Word -> Word -> Double

(Real b0, Distribution (Poisson b0) Int64) => CDF (Poisson b0) Int64

Methods

cdf :: Poisson b0 Int64 -> Int64 -> Double

(Real b0, Distribution (Poisson b0) Int32) => CDF (Poisson b0) Int32

Methods

cdf :: Poisson b0 Int32 -> Int32 -> Double

(Real b0, Distribution (Poisson b0) Int16) => CDF (Poisson b0) Int16

Methods

cdf :: Poisson b0 Int16 -> Int16 -> Double

(Real b0, Distribution (Poisson b0) Int8) => CDF (Poisson b0) Int8

Methods

cdf :: Poisson b0 Int8 -> Int8 -> Double

(Real b0, Distribution (Poisson b0) Int) => CDF (Poisson b0) Int

Methods

cdf :: Poisson b0 Int -> Int -> Double

(Real b0, Distribution (Poisson b0) Integer) => CDF (Poisson b0) Integer

Methods

cdf :: Poisson b0 Integer -> Integer -> Double

CDF (Poisson b0) Integer => CDF (Poisson b0) Double

Methods

cdf :: Poisson b0 Double -> Double -> Double

CDF (Poisson b0) Integer => CDF (Poisson b0) Float

Methods

cdf :: Poisson b0 Float -> Float -> Double

(CDF (Bernoulli b) Bool, RealFloat a) => CDF (Bernoulli b) (Complex a)

Methods

cdf :: Bernoulli b (Complex a) -> Complex a -> Double

(CDF (Bernoulli b) Bool, Integral a) => CDF (Bernoulli b) (Ratio a)

Methods

cdf :: Bernoulli b (Ratio a) -> Ratio a -> Double